1. Badges are handles by the built-in Badges add-on and Ranks are handled by the Ranks add-on. Both are enabled on the myCRED > Add-ons page. You can also find a setup guide for myCRED in the codex.

2. Yes this is possible thanks to what I call “template tags” these custom tags are replaced dynamically by myCRED with it’s current value. So for example %post_title% will be replaced with the post’s title. You can find all post related template tags in the codex. You use these tags in your log template fields when you setup for example a hook.

3. You can style notifications via your theme’s styles.css file.
If you go to the myCRED > Settings page and look under Notifications you can select to disable the default styling and apply everything yourself or just override the styling via your theme’s styles.css file.